Computer Aided Geometric Design
Mean value coordinates for closed triangular meshes
ACM SIGGRAPH 2005 Papers
Computer Aided Geometric Design - Special issue: Geometric modelling and differential geometry
Mean value coordinates for arbitrary planar polygons
ACM Transactions on Graphics (TOG)
A geometric construction of coordinates for convex polyhedra using polar duals
SGP '05 Proceedings of the third Eurographics symposium on Geometry processing
Spherical barycentric coordinates
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
On transfinite barycentric coordinates
SGP '06 Proceedings of the fourth Eurographics symposium on Geometry processing
A unified, integral construction for coordinates over closed curves
Computer Aided Geometric Design
Improving continuity of Voronoi-based interpolation over Delaunay spheres
Computational Geometry: Theory and Applications
A unified, integral construction for coordinates over closed curves
Computer Aided Geometric Design
Transfinite mean value interpolation
Computer Aided Geometric Design
Mesh parameterization: theory and practice
ACM SIGGRAPH ASIA 2008 courses
Maximum entropy coordinates for arbitrary polytopes
SGP '08 Proceedings of the Symposium on Geometry Processing
Polyhedral finite elements using harmonic basis functions
SGP '08 Proceedings of the Symposium on Geometry Processing
Discrete harmonic functions from local coordinates
Proceedings of the 12th IMA international conference on Mathematics of surfaces XII
GMP'08 Proceedings of the 5th international conference on Advances in geometric modeling and processing
Computer Aided Geometric Design
Visualising many-objective populations
Proceedings of the 14th annual conference companion on Genetic and evolutionary computation
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Barycentric coordinates are a fundamental concept in computer graphics and geometric modeling. We extend the geometric construction of Floater's mean value coordinates [Floater, M.S., Kos, G., Reimers, M., 2005. Mean value coordinates in 3d. Computer Aided Geometric Design 22 (7) (2005) 623-631; Ju, T., Schaefer, S., Warren, J., 2005a. Mean value coordinates for closed triangular meshes. In: Proceedings of ACM SIGGRAPH 2005] to a general form that is capable of constructing a family of coordinates in a convex 2D polygon, 3D triangular polyhedron, or a higher-dimensional simplicial polytope. This family unifies previously known coordinates, including Wachspress coordinates, mean value coordinates and discrete harmonic coordinates, in a simple geometric framework. Using the construction, we are able to create a new set of coordinates in 3D and higher dimensions and study its relation with known coordinates. We show that our general construction is complete, that is, the resulting family includes all possible coordinates in any convex simplicial polytope.